IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v24y1995i4p365-373.html
   My bibliography  Save this article

A double-integral equation for the average run length of a multivariate exponentially weighted moving average control chart

Author

Listed:
  • Rigdon, Steven E.

Abstract

The multivariate exponentially weighted moving average control chart is a control charting scheme that uses weighted averages of previously observed random vectors. This scheme, which is defined using Z0 = [mu]0, Zi = rXi + (1 - r)Zi - 1 (i [greater-or-equal, slanted] 1), where X1, X2, ... denote the vector-valued output of a process, can be used to detect shifts in the process mean vector more quickly, on the average, than the usual Hotelling T2 chart. We prove that for the special case [mu] = 0, [Sigma] = I, the average run length (ARL) depends on the initial value z0 for the MEWMA statistic only through its magnitude and the angle it makes with the mean vector. This theorem is then used to derive an integral equation of the ARL. This integral equation involves a double integral, and the unknown function is a function of two variables. ARLs can be obtained by approximating the solution to the integral equation. Previously, simulation was needed to approximate the ARLs.

Suggested Citation

  • Rigdon, Steven E., 1995. "A double-integral equation for the average run length of a multivariate exponentially weighted moving average control chart," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 365-373, September.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:4:p:365-373
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(94)00196-F
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lianjie Shu & Wenpo Huang & Wei Jiang, 2014. "A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 223-237, April.
    2. Amir Ahmadi-Javid & Mohsen Ebadi, 2017. "Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)," Papers 1708.06160, arXiv.org.
    3. Ming Lee & Michael Khoo, 2014. "Design of a multivariate exponentially weighted moving average control chart with variable sampling intervals," Computational Statistics, Springer, vol. 29(1), pages 189-214, February.
    4. Amir Ahmadi-Javid & Mohsen Ebadi, 2021. "Economic design of memory-type control charts: The fallacy of the formula proposed by Lorenzen and Vance (1986)," Computational Statistics, Springer, vol. 36(1), pages 661-690, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:24:y:1995:i:4:p:365-373. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.